By Duncan Steel 01/05/2020

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Did you know that the top of Mount Cook is by no means New Zealand’s furthest point from the centre of the Earth? And that Samoa’s tallest mountain is seven kilometres further from our planet’s core than anywhere in NZ? The highest point anywhere, in terms of separation from Earth’s centre? — It’s not Mount Everest.

It’s the sort of question that gets asked as a tie-breaker in a pub quiz: I am stood on the point on Earth’s surface that is furthest from its centre. My feet are two-feet apart (of course) along a north-south line. Which country is each foot in?

Cue for head-scratching and debate. Most people think that the point in question is the top of Mount Everest, and some know the border between Nepal and Tibet (as claimed by China) goes through that peak. In consequence a lot of the quizzers imagine that the question revolves around whether Tibet is a separate nation or not.

Actually, the answer is Ecuador. Both feet are in Ecuador. The location in question is the top of Mount Chimborazo, a volcano in the Andes that last erupted about 1,500 years ago. That’s the point on Earth’s surface that is further from our planet’s centre than any other.

The trick, as such, is in the way the question was phrased: furthest from Earth’s centre, rather than a mountain’s altitude above sea level. Compared to the planet’s geometrical centre, sea level varies by more than 21 km between the equator and the poles. At latitudes near the equator (such as that of Chimborazo: the name of Ecuador gives it away) the land and sea surfaces are about ten kilometres further from the planet’s core than at mid-latitudes like those of New Zealand… and ten kilometres is more than the height of even Mt Everest.

For completeness, let’s do the sums. First, let me say this: I will assume hereunder that, rather than mean sea level (MSL), all mountain heights can be referred instead to the reference ellipsoid that is used to describe the overall shape of the Earth. This is termed WGS84 (World Geodetic System 84). This makes it easy to calculate an Earth radius at any latitude, varying from 6378.137 km at the equator down to 6356.752 km at the poles. Rather than being a simple ellipsoid, MSL describes a geoid which depends on local variations in gravity (due to denser rocks, or mountain ranges) and also the spin of the planet. Across the whole of Earth’s surface MSL varies by up to about 100 metres in either direction, compared to WGS84. In view of that, the accuracy of the figures I derive below should not be assumed to extend to as good as ten metres; I will give final kilometre figures terminating in the second decimal place, then, but don’t put too much faith in that last numeral.

Mount Everest: Altitude 8,848 metres. Latitude very close to 28 degrees, where Earth’s radius r  (from WGS84) is 6373.46 km. The distance of its summit from the centre of the planet is therefore R = 6382.31 km.

Mount Chimborazo: Altitude 6,263 metres. Latitude about 1.47 degrees (and south, by the way). There, r = 6378.12, and so R = 6384.38 km. That’s fully two kilometres greater than the value for Mount Everest, and so informs you where you really need to go if you want to stand on top of the world.

The Top of New Zealand: Where?

I reckon that most readers will be able to see where this is going, when they read that heading just above. Everyone knows that Mount Cook/Aoraki is the tallest mountain in NZ (despite having a sudden reduction in height when the top fell off in 1991)… but if you stood on its peak, are you the furthest from Earth’s centre you can be in NZ, and therefore on top of the nation?

Rhetorical question, the answer as we will see being no. But before getting on to the relevant sums, another pub quiz question that I recall actually being posed whilst I was living in Christchurch back in the 1980s. How far south of Christchurch do you need to go until you reach the same latitude as Mount Cook?  I heard answers of Ashburton, then Timaru, and even Oamaru. In reality, if you tootle through the tunnel to Lyttelton you’ve reached a latitude further south than Mt Cook. If you were heading to Lincoln, you’ve passed Mt Cook’s latitude as you drive through Halswell or Prebbleton.

In my mind, knowledge of NZ’s geography is confused by calling the two main land masses North Island and South Island. In reality they are the Northeast Island, and the Southwest Island. Where I sit in Nelson, it happens that I am at a more-northern latitude than Wellington. The islands are tilted: I had to rotate the image in the graphic at the head of this blog post to fit it in nicely. Perhaps a wider acceptance of the te reo Māori names — Te Ika-a-Māui and Te Waipounamu — would assist.

Back to NZ’s mountains: the upwards component of our geography, rather than the sideways north-south-east-west mapping.

A revision a decade or so ago (quite apart from the avalanche in 1991 that physically-reduced its height) placed Mount Cook’s altitude as 3,724 metres. Yes, that’s the tallest mountain in NZ, compared to sea level. At its latitude of near 43.6 degrees Earth’s radius is 6368.01 km, according to the WGS84 model. This means its peak is 6371.73 km from Earth’s centre.

Heading south to Mount Aspiring/Tititea, similar sums result in finding its summit is 6370.75 km from Earth’s centre: almost a full kilometre less than Aoraki, despite Tititea being only 700 metres shorter than Mt Cook. Further south, the less the Earth’s radius.

So let’s head north, to where Earth’s radius is larger. Tapuae-o-Uenuku (formerly Mount Tapuaenuku) in the Inland Kaikoura Ranges has a latitude close to 42 degrees, and an altitude of 2,884 metres. This results in a value of R = 6371.49 km, just 240 metres less than the distance of Mt Cook’s summit from Earth’s centre.

Whilst it might offend South Island/Mainland parochialism, skipping northwards we might consider first Mount Egmont/Taranaki. Its latitude is near 39.3 degrees, and its altitude 2,518 metres. Boosted by the increased radius at this reduced latitude, the peak of this volcano is 6372.12 km from the centre of the Earth. You read that right: almost 400 metres greater than the top of Mt Cook.

We can do better, though. Mount Ruapehu is at almost exactly the same latitude as Mt Egmont, and has been measured to be 2,797 metres high. This results in R = 6372.40 km being its separation from Earth’s centre, 670 metres more than Mt Cook.

The bottom line (that’s a joke, by the way): head for the central North Island and Tongariro National Park if you want to stand on the very top of New Zealand. Just be warned that a major eruption of Mt Ruapehu might change these figures.

Just how flat is Australia?

While Australia (the West Island) clearly exceeds NZ by far in terms of lateral extent, if one considers mountain heights our active geology has led to there being many, many peaks in NZ that are far taller than Australia can boast.

Another pub quiz question from my time living there, where again one needs to listen carefully as the poser is read out amongst the din of the diners and imbibers: Which is the tallest mountain in Australian territory?

It’s the final word that is significant there. The highest mountain in Australia itself is Mount Kosciuszko in the Snowy Mountains, at just 2,228 metres above sea level. You can get a chairlift from Thredbo to achieve most of the climb needed, then it’s a fairly straightforward amble on a formed track that leads to a bit of a push to achieve the final spiral walkway to the top. Australia owns some territory down in the southern Indian Ocean, though, and Mawson Peak on Heard Island is more than 500 metres higher, at 2,745 m.

Heard Island is a long way south, however, where Earth’s radius is smaller. The top of Mawson Peak (by the way, I once had an asteroid named for Sir Douglas Mawson, but that’s a different story) is at R = 6367.25 km, whereas Mount Kosciuszko (careful with the spelling) towers above it at = 6372.86 km, five-and-a-half kilometres further from the centre of the Earth.

Pacific island peaks

Most of us think of the various Pacific islands as being mainly low-lying atolls. As an astronomer, I am familiar with the extreme elevations to be found in Hawai’i, in particular the cluster of telescopes on Mauna Kea. But let us think of the other islands closer to home in the South Pacific.

The tallest peak in the Solomons is Mount Popomanaseu at 2,335 metres. So close to the equator, it achieves R = 6379.87 km. Take that, Mount Cook!

Other island nations have central mountains that are lower, yet still far exceed Mt Cook in terms of distance from Earth’s centre. In Tahiti, Mount Orohena is 2,241 m high, the top being at R = 6378.45 km. In Vanuatu, the tallest peak is Mount Tabwemasana at 1,879 metres, but R = 6378.53 km. Finally, in Samoa Mount Silisili is 1,858 m high, resulting in R = 6378.82 km at its latitude.

My actual bottom line, then: surprisingly enough, Samoa’s tallest mountain has a summit that is more than seven kilometres further from the centre of the Earth than the peak of Mount Cook/Aoraki. Strange, but true.